# On Kernel Derivative Approximation with Random Fourier Features

arXiv: https://arxiv.org/abs/1810.05207 · HTML: https://mlsanity.com/paper/1810.05207/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2018.

## Built on by (most cited first, 6 of 6)

- [Generalization Bounds for Sparse Random Feature Expansions](https://mlsanity.com/paper/2103.03191/) (2021)
- [Learning to Forecast Dynamical Systems from Streaming Data](https://mlsanity.com/paper/2109.09703/) (2021)
- [Learning a Fourier Transform for Linear Relative Positional Encodings in Transformers](https://mlsanity.com/paper/2302.01925/) (2023)
- [Random Fourier Signature Features](https://mlsanity.com/paper/2311.12214/) (2023)
- [Random Feature Representation Boosting](https://mlsanity.com/paper/2501.18283/) (2025)
- [Learning Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces and Random Features](https://mlsanity.com/paper/2404.07703/) (2024)

## Abstract (arXiv)

Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood theoretically on their optimality and limitations of their performance. Only recently, precise statistical-computational trade-offs have been established for RFFs in the approximation of kernel values, kernel ridge regression, kernel PCA and SVM classification. Our goal is to spark the investigation of optimality of RFF-based approximations in tasks involving not only function values but derivatives, which naturally lead to optimization problems with kernel derivatives. Particularly, in this paper, we focus on the approximation quality of RFFs for kernel derivatives and prove that the existing finite-sample guarantees can be improved exponentially in terms of the domain where they hold, using recent tools from unbounded empirical process theory. Our result implies that the same approximation guarantee is attainable for kernel derivatives using RFF as achieved for kernel values.